Logical realism is a view about the metaphysical status of logic, but it comes in many forms. Common to most if not all the views captured by the label “logical realism” is that logical facts are mind- and language-independent. But that does not entail anything about the nature of logical facts or about our epistemic access to them. Another open question is whether logical realism entails logical monism, the view that there is one true logic, or whether it is compatible with some forms of logical pluralism. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some of the challenges that these views face.